Question: Simplify to lowest terms. $\dfrac{12}{32}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 12 and 32? $12 = 2\cdot2\cdot3$ $32 = 2\cdot2\cdot2\cdot2\cdot2$ $\mbox{GCD}(12, 32) = 2\cdot2 = 4$ $\dfrac{12}{32} = \dfrac{3 \cdot 4}{ 8\cdot 4}$ $\hphantom{\dfrac{12}{32}} = \dfrac{3}{8} \cdot \dfrac{4}{4}$ $\hphantom{\dfrac{12}{32}} = \dfrac{3}{8} \cdot 1$ $\hphantom{\dfrac{12}{32}} = \dfrac{3}{8}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{12}{32}= \dfrac{2\cdot6}{2\cdot16}= \dfrac{2\cdot 2\cdot3}{2\cdot 2\cdot8}= \dfrac{3}{8}$